Completed by positioning the following containers on the order confirmation page:

<body>
...
<!-- Add this div tag anywhere in the order confirmation page to render the game plugin -->
<div id="lcgame" runat="server"></div>
</div>
...
<!-- Add this div tag at the bottom of the page (in order not to interfere with page loading) -->
<div id="lcscript" runat="server"></div>
</body>